Annales Academię Scientiarum Fennicę
Mathematica
Volumen 34, 2009, 215-232
University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; vasileios.chousionis 'at' helsinki.fi
Abstract. The aim of the present paper is twofold. We study directed porosity in connection with conformal iterated function systems (CIFS) and with singular integrals. We prove that limit sets of finite CIFS are porous in a stronger sense than already known. Furthermore we use directed porosity to establish that truncated singular integral operators, with respect to general Radon measures \mu and kernels K, converge weakly in some dense subspaces of L2(\mu) when the support of \mu belongs to a broad family of sets. This class contains many fractal sets like CIFS's limit sets.
2000 Mathematics Subject Classification: Primary 28A80, 42B20.
Key words: CIFS, porosity, singular integrals.
Reference to this article: V. Chousionis: Directed porosity on conformal iterated function systems and weak convergence of singular integrals. Ann. Acad. Sci. Fenn. Math. 34 (2009), 215-232.
Copyright © 2009 by Academia Scientiarum Fennica